{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f90b3401",
   "metadata": {},
   "source": [
    "# 分布基础"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef64f330",
   "metadata": {},
   "source": [
    "尖峰：一个分布的峰值>正态分布\n",
    "\n",
    "中峰：=\n",
    "\n",
    "低峰： <"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "588ec41d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "883b71e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def std_plot():\n",
    "    \"\"\"\n",
    "    draw standard deviation normal distribution\n",
    "    \"\"\"\n",
    "    mu = 0.0    # mean\n",
    "    sd = 1.0    # std\n",
    "    sd2 = 2.0\n",
    "    sd3 = 3.0\n",
    "\n",
    "    # red line\n",
    "    x = np.linspace(mu - 3 * sd, mu + 3 * sd, 50) # x range\n",
    "    y = stats.norm.pdf(x)\n",
    "    plt.plot(x, y, \"r\", linewidth = 2)\n",
    "\n",
    "    # green line\n",
    "    x2 = np.linspace(mu - 6 * sd, mu + 6 * sd, 50) # x range\n",
    "    y2 = stats.norm.pdf(x2, mu, sd2)\n",
    "    plt.plot(x2, y2, \"g\", linewidth = 2)\n",
    "\n",
    "    # blue line\n",
    "    x3 = np.linspace(mu - 10 * sd, mu + 10 * sd, 50) # x range\n",
    "    y3 = stats.norm.pdf(x3, mu, sd3)\n",
    "    plt.plot(x3, y3, \"b\", linewidth = 2)\n",
    "\n",
    "    plt.grid(True)  # 显示网格线\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4f06a94b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "std_plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5a0adaf0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "389f9e9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def kurtosis(a):\n",
    "    \"\"\"\n",
    "    Compute the sample kurtosis of a data set.\n",
    "    :param a array_like\n",
    "    :return kurtosis of sample\n",
    "    \"\"\"\n",
    "    return stats.kurtosis(a, bias=False)\n",
    "\n",
    "\n",
    "def main():\n",
    "    data = np.array([25.78, 15.05, 4.26, 19.14, 3.30, -35.75, 25.62, 15.15, -0.72, 17.25])\n",
    "    print(\"kurtosis:\", kurtosis(data))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ccad3dc3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "kurtosis: 4.093384492658573\n"
     ]
    }
   ],
   "source": [
    "# 该值大于0，所以是尖峰厚尾分布的\n",
    "main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f9f2a4b7",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
